Mathematics of the people, for the people, by the people: encouraging mathematical happiness.
Joined October 2009
- Tweets 28,255
- Following 4,753
- Followers 157,172
- Likes 524
5,755 Photos and videos
18 Jul 2025
Hi everyone - I've opened a BlueSky account: @republicofmath.bsky.social. See you there!
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23 Oct 2024
Geometric proofs of the irrationality of square-roots for select integers
arxiv.org/pdf/2410.14434
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Republic of Mathematics retweeted
7 May 2024
Hi! Next month I'm running a learning experience for K-12 teachers called "21st Century Mathematics". Its goal is to help teachers to connect the math they teach with some math that has been discovered in the 21st century.
Info register: justinlanier.org/21st-centur…
Pass it along!
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Republic of Mathematics retweeted
7 May 2024
Base b is "robust" if each fraction 1/2,1/3,..,1/(b-1) is a ratio of two integers expressed in base b that use each digit 1, 2, 3,.... (up to some value) exactly once. (1/b cannot be so expressed. Why?)
@iconjack shows base 10 is robust.
Base 3 and base 4 are robust. Base 5? 6?
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6 May 2024
Dominic Welsh's important contributions to probability and combinatorics: arxiv.org/pdf/2404.13942
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10 Oct 2023
Data from 350,757 coin flips provide strong evidence that when some (but not all) people flip a fair coin, it tends to land on the same side it started.
arxiv.org/pdf/2310.04153.pdf
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Republic of Mathematics retweeted
3 Oct 2023
N>1 cups all upright. A "move" consists of turning all but 2 cups over. (So, each move N-2 cups change state upright/upside-down.)
For which N is it possible to make all N cups upside-down?
[General theory about N cups and turning N-k over at a time?]
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Republic of Mathematics retweeted
20 Sep 2023
Square tiles in an NxM grid with one blank space. Tiles can slide H and V into the space.
Starting with a blue tile top right, blank space to its left ...
For which N and M is possible to make slides and have the blue tile visit each and every location in the grid?
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Republic of Mathematics retweeted
11 Sep 2023
An inf number of bags. First contains one Red & one White ball. Second 2R & 1W balls. Third 3R & 1W balls. I pull out a ball from first bag. If R, I win! If not, I go to second bag & pull out a ball. If R, I win! If not, on to next bag, and so on. Will I win? Expected # of turns?
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Republic of Mathematics retweeted
6 Sep 2023
This configuration of 16 triangles has perimeter 14. (Assume each triangle side length is 1.)
Remove triangles one at a time, always increasing perimeter. What's the least number of triangles you can get to? What is the final total perimeter of the configuration you have?
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5 Sep 2023
The sum of two cubes problem—an approach that’s classroom friendly
arxiv.org/pdf/2309.00162.pdf
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Republic of Mathematics retweeted
28 Aug 2023
Suppose you find n consecutive integers that sum to a square number r^2.
Prove that those n integers plus the next r integers added together equals the sum of the following r integers.
Moreover, prove that n integers after all that sum to (r n)^2 so that this process repeats.
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26 Jul 2023
So Twitter is now "X" - X the unknown? X the variable? X the place holder?
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26 Jul 2023
The Euclidean algorithm can be used to generate a very large family of rhythms, including rhythms in which the rests have a palindromic structure.
arxiv.org/pdf/2307.13120.pdf
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25 Jul 2023
You need 27 tickets to guarantee a win on the UK national lottery
arxiv.org/pdf/2307.12430.pdf
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19 Jun 2023
Right! Exams are a near sure way of ensuring that many students will cram and so forget what they supposedly "learned". Harry Bahrick wrote about this in the Oxford Handbook of Memory
19 Jun 2023
Something about the way we teach math is broken. We do review in September because kids have forgotten everything. They have forgotten it because it was mostly memorized to be tested.
Their brains--rightfully so--discard such trivial junk.
But, sure, let's carry on...@HumResPro
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19 Jun 2023
Apropos @jamestanton's story of walking on a 5x5 planar grid: youtu.be/b86QcxdrNF4, what about a 5x5 (or other ) grid on a torus (or other surfaces of higher genus)?
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9 Jun 2023
#FF for math @jamestanton @GlobalMathProj @magiaymates @cbrownLmath
@NaturalMath @stevenstrogatz @AlexKontorovich @TamasGorbe @monsoon0 @FryRSquared @mathyawp @octonion @MathforLove @k8nowak @maanow @Derektionary @neil_calkin @Mathgarden @ilana_horn @MrHonner @wilderlab
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